Probability..

Tipsandtricks.

4 big ideas(question types)

1........ pathway problem.
- pascals triangle(be able to create it)

2.......... fundamental counting principle.
-nPr ------------------------------ math over 1 prb
(big #) order matters,
ex: books on a shelf in a different orders
: licence plates
: phone #
: locker combo
= n! / (n-r)!

-nCr
(small #) order doesnt matter,
n!/(n-r)!*r!
ex:
:pizza toppings
:committees

SHOW ALL WORK (sample space ... )

3..............INDEPENDENT / DEPENDENT
* denominator changes through the question chronologically

dependant >> without replacement
independent>> replacement

**consider tree diagram

4.............MUTUALLY INCLUSIVE vs MUTUALLY EXCLUSIVE

inclusive >> P(A or B) = P(A) + P(B) - P(A and B)
exlusive(they cant happen at the same time)>> P(A or B)=P(A)+P(B)




****COMPLEMEMTARY.. FORMULA.
P(not exactly 1 head)= 1-P(exactly one head)

vector exam review.

one or both of these type of problems

1. parellelogram, simple resultant.
used in these circumstances :
- two forces acting on a stationary something
-simultaneous vectors
(same time)
-magnitudes of vectors and only angle between them

2.... OR questions... "open response"
- means that there is no specific correct answer to the problem but rather many possible correct answers that satisfy the requirements of the problem.
** look for 4 or more marks.

3..... conversion/speed

ex. diver on the ocean floor
14 m/s for 3 mins = 2520m

Make origins.... when using triangle methods.

exam review

matrix modelling

What will i be expected to do?

** do not do anything WITHOUT a calculator.
depend on your calc. **

Questions to expect.
1...... maybe 1 to 2 multiple choice and one longer answer.
(MATRIX OPERATIONS) -> add, subtract, multiply(scalar * multiplying it by one number ) , multiply (matrix multiplication -> one matrix times another one)

2.... TRANSITION MATRIX question
(switching behaviour over time)
** are always n by n (SQUARE)
** rows add up to 1.0 (use decimals)
Also - "initial condition matrices must be row matrices in the form 1 by n.
- set the one up by 1 by 3; then the changes in a 3 by 3.
to show stability.... times matrix a * b ... times them by 99(ex) to the power... then add one and if its the same number... then stability is reached.

3.... MATRIX MULTIPLICATION as a word problem
-> probably something like inventory problem.
-> remember to avoid nonsense calculations (answer has no meaning.)

4.....NETWORK/MATRIX question
-> (# of routes to plan, for instance, transportation)


Show the matrix operations to calculate the number of trails from one town to another passing through at most two other towns. Do not solve.

A + A squared + A cubed
direct + through one town + through 2 towns